Question

how many gallons will it take to mow a lawn if you maintain the rate of 1/2 gallon of gasoline per 1/4 mowed

Answer 1

Recall that one whole is 1, or in this case since the denominator is 4, then 4/4 is 1 whole, so the whole lawn is 4/4.

$\bf \begin{array}{ccll} gallons&mowed\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{1}{2}&\frac{1}{4}\\\\ g&\frac{4}{4} \end{array}\implies \cfrac{\frac{1}{2}}{g}=\cfrac{\frac{1}{4}}{\frac{4}{4}}\implies \cfrac{\frac{1}{2}}{\frac{g}{1}}=\cfrac{\frac{1}{4}}{\frac{4}{4}}\implies \cfrac{1}{2}\cdot \cfrac{1}{g}=\cfrac{1}{4}\cdot \cfrac{4}{4} \\\\\\ \cfrac{1}{2g}=\cfrac{1}{4}\implies 4=2g\implies \cfrac{4}{2}=g\implies 2=g$